Ohio State University Algebraic Geometry Seminar 

  Year 2018-2019

Time: Tuesdays 3-4pm
Location: MW 154

Schedule of talks:


 

TIME  SPEAKER TITLE
August 21  
Tue, 3pm 
Hsian-Hua Tseng 
(OSU) 
The descendant Hilb/Sym correspondence for the plane
September 4  
Tue, 3pm 
Rachel Webb 
(Michigan) 
The Abelian-Nonabelian Correspondence for Quasimap I-functions
October 2  
Tue, 4:15pm
Ruth Charney 
(Brandeis) 
Rado Lecture Series 2018
October 9  
Tue, 3pm 
Angelica Cueto 
(OSU) 
Anticanonical tropical del Pezzo cubic surfaces contain exactly 27 lines
October 16  
Tue, 3pm 
Harry Richman 
(U Michigan) 
Equidistribution of tropical Weierstrass points
October 23  
Tue, 3pm 
Daniel Hast 
(Rice) 
Rational points and unipotent fundamental groups
October 30  
Tue, 3pm 
Pengyu Yang 
(OSU) 
Rational points on homogeneous varieties
November 6  
Tue, 3pm 
TBA 
() 
TBA
November 13  
Tue, 3pm 
TBA 
() 
TBA
November 20  
Tue, 3pm 
TBA 
() 
TBA
November 27  
Tue, 3pm 
Brooke Ullery 
(Harvard) 
TBA
December 4  
Tue, 3pm 
Brent Doran 
(Oxford) 
TBA
January 8  
Tue, 3pm 
TBA 
() 
TBA
January 15  
Tue, 3pm 
TBA 
() 
TBA
January 22  
Tue, 3pm 
Graham Denham 
(Western Ontario) 
TBA
January 29  
Tue, 3pm 
TBA 
() 
TBA
February 5  
Tue, 3pm 
TBA 
() 
TBA
February 12  
Tue, 3pm 
TBA 
() 
TBA
February 19  
Tue, 3pm 
TBA 
() 
TBA
February 26  
Tue, 3pm 
TBA 
() 
TBA
March 5  
Tue, 3pm 
TBA 
() 
TBA
March 7  
Thurs, 4:15pm
TBD
Valery Lunts 
(Indiana) 
Colloquium
March 12  
Tue, 3pm 
(break)  
 
March 19  
Tue, 3pm 
TBA 
() 
TBA
March 25-27  
Tue, 4:10pm
TBD
Pavel Etingof 
(MIT) 
Zassenhaus Lecture Series 2019
April 2  
Tue, 3pm 
TBA 
() 
TBA
April 9  
Tue, 3pm 
TBA 
() 
TBA

Abstracts


(Tseng): Let S be a nonsingular surface. A version of the crepant resolution conjecture predicts that the descendant Gromov-Witten theory of Hilbn(S), the Hilbert scheme of n points on S, is equivalent to the descendant Gromov-Witten theory of Symn(S), the n-fold symmetric product of S. In this talk we discuss how this works when S is C2. We explicitly identify a symplectic transformation equating the two descendant Gromov-Witten theories. We also establish a relationship between this symplectic transformation and the Fourier-Mukai transformation which identifies the (torus-equivariant) K-groups of Hilbn(C2) and Symn(C2). This is based on joint work with R. Pandharipande.


(Webb): When a complex reductive group G with maximal torus T acts on an affine variety S, one can form two (GIT) quotients: W//G and W//T. With the right hypotheses, W//G and W//T are both smooth projective varieties. The relationship between the cohomology rings of these two varieties is well understood. I will discuss the relationship of their quantum cohomology using the quasimap theory of Ciocan-Fontanine and Kim. In particular, I will present the abelian-nonabelian correspondence for quasimap I-functions when W is a vector space and G is connected.


(Cueto): Since the beginning of tropical geometry, a persistent challenge has been to emulate tropical versions of classical results in algebraic geometry. The well-know statement "any smooth surface of degree three in P3 contains exactly 27 lines'' is known to be false tropically. Work of Vigeland from 2007 provides examples of tropical cubic surfaces with infinitely many lines and gives a classification of tropical lines on general smooth tropical surfaces in TP3. In this talk I will explain how to correct this pathology by viewing the surface as a del Pezzo cubic and considering its embedding in P44 via its anticanonical bundle. The combinatorics of the root system of type E6 and a tropical notion of convexity will play a central role in the construction. This is joint work in progress with Anand Deopurkar.


(Richman): The set of (higher) Weierstrass points on a curve of genus g > 1 is an analogue of the set of N-torsion points on an elliptic curve. As N grows, the torsion points "distribute evenly" over a complex elliptic curve. This makes it natural to ask how Weierstrass points distribute, as the degree of the corresponding divisor grows. We will explore how Weierstrass points behave on tropical curves (i.e. finite metric graphs), and explain how their distribution can be described in terms of electrical networks. Knowledge of tropical curves will not be assumed, but knowledge of how to compute resistances (e.g. in series and parallel) will be useful.


(Hast): Given a curve of genus at least 2 over a number field, what can we say about its set of rational points? Faltings' theorem tells us that this set is finite, but many questions remain about how to obtain good bounds on the number of rational points and how to provably list all rational points. We will survey some recent progress and ongoing work on these questions using Kim's non-abelian Chabauty method, which uses the fundamental group to construct p-adic analytic functions that vanish on the set of rational points.
In particular, we present a new proof of Faltings' theorem for superelliptic curves over Q, due to joint work with Jordan Ellenberg. We will also discuss a conditional generalization of this strategy from Q-points to points in any real number field.


(Yang): Given a Fano variety X over a number field, and a height function on X. Manin's conjecture predicts the asymptotic growth of the number of rational points on X of bounded height. When X is an equivariant compactification of a homogeneous variety, the conjecture is related to equidistribution of adelic periods. We will discuss some recent progress in this direction.


(Ullery):


(Doran):


(Denham):


Past Seminars

Ohio State University Algebraic Geometry Seminar-Year 2017-2018

Ohio State University Algebraic Geometry Seminar-Year 2016-2017

Ohio State University Algebraic Geometry Seminar-Year 2015-2016

Ohio State University Algebraic Geometry Seminar-Year 2014-2015

Ohio State University Algebraic Geometry Seminar-Year 2013-2014


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